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Autor Villanueva, Ignacio |
Documentos disponibles escritos por este autor (48)
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We show that, for every orthogonally additive homogeneous polynomial P on a space of continuous functions C(K) with values in a Banach space Y, there exists a linear operator S : C(K) -> Y such that P(f) = S(f(n)). This is the C(K) version of a[...]![]()
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We show that, for bounded sequences in C(K,E), the polynomial sequential convergence is not equivalent to the pointwise polynomial sequential convergence. We introduce several conditions on E under which different versions of the result are true[...]![]()
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Villanueva, Ignacio ; Peralta Pereira, Antonio Miguel ; Wright, J. D. Maitland ; Ylinen, Kari | Cambridge University Press | 2010-05We introduce the concept of quasi-completely continuous multilinear operators and use this concept to characterize, for a wide class of Banach spaces X1, …, Xk, the multilinear operators T : X1 × … × Xk ? X with an X-valued Aron–Berner extension.![]()
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We characterize the positive radial continuous and rotation invariant valuations V defined on the star bodies of Rn as the applications on star bodies which admit an integral representation with respect to the Lebesgue measure. That is,V(K)=?Sn?[...]![]()
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We show that a radial continuous valuation defined on the n-dimensional star bodies extends uniquely to a continuous valuation on the n-dimensional bounded star sets. Moreover, we provide an integral representation of every such valuation, in te[...]![]()
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González-Guillén, Carlos E. ; Lancien, Cécilia ; Palazuelos Cabezón, Carlos ; Villanueva, Ignacio | Springer | 2017It is now a well-known fact that the correlations arising from local dichotomic measurements on an entangled quantum state may exhibit intrinsically non-classical features. In this paper we delve into a comprehensive study of random instances of[...]![]()
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The purpose of this paper is to characterise the class of regular continuous multilinear operators on a product of C(K) spaces, with values in an arbitrary Banach space. This class has been considered recently by several authors in connection wi[...]![]()
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We clarify and prove in a simpler way a result of Taskinen about symmetric operators on C(K-n), K an uncountable metrizable compact space. To do this we prove that, for any compact space K and any n is an element of N, the symmetric injective n-[...]![]()
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We present a Riesz type representation theorem for multilinear operators defined on the product of C(K,X) spaces with values in a Banach space. In order to do this we make a brief exposition of the theory of operator valued polymeasures.[RESUMEN[...]![]()
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González-Guillén, C.E. ; Jimenez, C.H. ; Palazuelos Cabezón, Carlos ; Villanueva, Ignacio | Springer | 2016It is well known that quantum correlations for bipartite dichotomic measurements are those of the form (Formula presented.), where the vectors ui and vj are in the unit ball of a real Hilbert space. In this work we study the probability of the n[...]![]()
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Villanueva, Ignacio ; Bombal Gordón, Fernando ; Fernández Unzueta, M. | Polish Acad Sciencies Inst Mathematics | 2001The authors obtain in this paper a classification of projective tensor products of C(K) spaces, in terms of the behaviour of certain classes of multilinear operators on the product of the spaces, or the verification of certain Banach space prope[...]![]()
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We present some results concerning the general theory of polymeasures. Among them, we point out an example of a polymeasure of bounded semivariation and unbounded variation, and two different characterizations of uniform polymeasures.![]()
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What can we say about the spectra of a collection of microscopic variables when only their coarse-grained sums are experimentally accessible? In this paper, using the tools and methodology from the study of quantum nonlocality, we develop a math[...]![]()
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A Banach space X has the Dunford–Pettis property (DPP) if and only if whenever (xn) and (pn) are weakly null sequences in X and X*, respectively, we have pn(xn)? 0. Freedman introduced a stricly weaker version of the DPP called the alternative D[...]![]()
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Peralta Pereira, Antonio Miguel ; Villanueva, Ignacio ; Wright, J. D. Maitland ; Ylinen, Kari | Elsevier | 2007-01-15Let X be a Banach space. Then there is a locally convex topology for X, the “Right topology,” such that a linear map T, from X into a Banach space Y, is weakly compact, precisely when T is a continuous map from X, equipped with the “Right” topol[...]![]()
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Villanueva, Ignacio ; Junge, Marius ; Pérez García, David ; Wolf, Michael ; Palazuelos Cabezón, Carlos | Springer | 2008We prove that there are tripartite quantum states (constructed from random unitaries) that can lead to arbitrarily large violations of Bell inequalities for dichotomic observables. As a consequence these states can withstand an arbitrary amount [...]![]()
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Villanueva, Ignacio ; Junge, Marius ; Pérez García, David ; Wolf, Michael ; Palazuelos Cabezón, Carlos | Springer | 2010-12In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order ?(?n?Log2n) when observables with n possible outcomes are used. A central tool in the analysis is a close[...]![]()
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Junge, M. ; Pérez García, David ; Palazuelos Cabezón, Carlos ; Villanueva, Ignacio ; Wolf, Michael | Springer | 2010In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order $\sqrt{n}$ (up to a logarithmic factor) when observables with n possible outcomes are used. A central tool[...]![]()
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Villanueva, Ignacio ; Pérez García, David | Matematisk Institut, Universitetsparken NY Munkegade | 2005We prove that a tensor norm alpha (defined on tensor products of Hilbert spaces) is the Hilbert-Schmidt norm if and only if l(2) circle times(...)circle times l(2), endowed with the norm alpha, has an unconditional basis. This extends a classica[...]![]()
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We introduce a notion of unconditionally converging multilinear operator which allows to extend many of the results of the linear case to the multilinear case. We prove several characterizations of these multilinear operators (one of which seems[...]![]()
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Villanueva, Ignacio ; Pérez García, David ; Cabello Sánchez, Félix | Oxford University Press | 2006-10We describe complemented Copies Of l(2) both in C(K-1)circle times C-pi(K-2) when at least one of the compact spaces K-i is not scattered and in L-1(mu(1))circle times L-is an element of(1)(mu(2)) when at least one of the measures is not atomic.[...]![]()
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Villanueva, Ignacio ; Peralta Pereira, Antonio Miguel ; Wright, J. D. Maitland ; Ylinen, Kari | Cambridge University Press | 2010The strong* topology s_(X) of a Banach space X is defined as the locally convex topology generated by the seminorms x 7! kSxk for bounded linear maps S from X into Hilbert spaces. The w-right topology for X, _(X), is a stronger locally convex to[...]![]()
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Using a ‘reasonable’ measure in , the space of 2-homogeneous polynomials on ?1n, we show the existence of a set of positive (and independent of n) measure of polynomials which do not attain their norm at the vertices of the unit ball of ?1n. Ne[...]